1. Field of the Invention
The invention relates to the field of photonic crystals and their applications in optics and microwave technology. More specifically, the invention relates to nonreciprocal magnetic photonic crystals, including magnetic multilayered structures, with magnetic constituent being a gyrotropic material with appreciable Faraday rotation.
2. Description of the Prior Art
Photonic crystals comprise various spatially periodic structures composed of the constituents each of which is practically lossless for electromagnetic radiation in the frequency range of interest. As a consequence of spatial periodicity, the electromagnetic frequency spectrum of photonic crystals develops a band-gap structure similar to that of electrons in semiconductors and metals. The existence of forbidden frequency gaps (stop-bands) in the electromagnetic spectrum forms the basis for the majority of photonic crystals applications in optics and microwave technology. Additional practically important feature of photonic crystals that has been utilized in a number of optical and microwave solid-state devices is the possibility to engineer photonic crystals with prescribed dispersion. This feature allows to control the direction and speed of electromagnetic wave propagation through composite media.
Another category of optical and microwave solid-state devices that can be seen as a prior art to the present invention, comprises various nonreciprocal devices and circuit elements. Some examples are presented by microwave and optical isolators, gyrators, rotators, nonreciprocal phase shifters, etc. Nonreciprocal solid-sate devices based on the effect of Faraday rotation in magnetic media are widely used in microwave and optics.
Nonreciprocal Magnetic Photonic Crystals
In gyrotropic photonic crystals, wave propagation can display additional features, utilization of which forms the basis of the present invention. In particular, in gyrotropic photonic crystals, electromagnetic waves propagating in two opposite directions may display strong asymmetry
xcfx89(k)xe2x89xa0xcfx89(xe2x88x92k),xe2x80x83xe2x80x83(1) 
as shown in FIG. 2.
The present invention utilizes the strong spectral asymmetry (1) of the bulk electromagnetic waves in gyrotropic photonic crystals. Unlike the case of surface electromagnetic waves, the spectral asymmetry of the bulk waves is prohibited by symmetry in all nonmagnetic and most magnetic photonic crystals. The strong spectral asymmetry though of the bulk waves has been shown to exist in gyrotropic photonic crystals with some special space arrangement of the constituents (A. Figotin and I. Vitebskiy, Phys. Rev. E, 2001). It can be achieved by proper space arrangement of its constitutive components. The spectral asymmetry by no means occurs automatically in any gyrotropic photonic crystal. Quite the opposite, only special periodic arrays of the gyrotropic and other components can produce the effect. For this reason, all magnetic photonic crystals considered in previous art, have perfectly symmetric bulk dispersion relations. The search for periodic arrays yielding strongly asymmetric dispersion relations constitutes an important part of the design.
Strong spectral asymmetry may result in the phenomenon of unidirectional wave propagation, which forms the physical basis of the present invention. Consider a plane wave propagating through a gyrotropic photonic crystal along the Z direction, so that both the wave group velocity u=∂xcfx89/∂k and the wave vector k are parallel to Z. Suppose that the electromagnetic dispersion relation is asymmetric, and that one of the spectral branches xcfx89(k) develops a stationary inflection point at k=k1 and xcfx89=xcexa9 as shown in FIG. 3
At k=k1: ∂xcfx89/∂k=0; ∂2xcfx89/∂k2=0; and ∂3xcfx89/∂k3xe2x89xa00xe2x80x83xe2x80x83(2) 
There are exactly two bulk electromagnetic modes associated with the frequency xcexa9, with the corresponding wave numbers being k1 and k2. Observe that only one of the two waves can transfer the energy, namely the one with k=k2 and the group velocity u(k2) greater than 0. Indeed, the backward wave with k=k1 has zero group velocity u(k1)=0 and does not propagate through the medium. Because of this property, we call the mode related to k=k1 the frozen mode, while a gyrotropic photonic crystal supporting the frozen mode is referred to as a unidirectional gyrotropic photonic crystal.
At first sight, the unidirectional photonic crystal would act similarly to a common microwave or optical isolator, transmitting radiation of the frequency xcexa9 only in one of the two opposite directions. But in fact, there is an important difference. An isolator simply eliminates (usually, absorbs or deflects) the wave propagating in the undesired direction, whereas the unidirectional photonic crystal, being transparent for electromagnetic wave propagating in one direction, freezes and accumulates the radiation of the same frequency xcexa9 propagating in the opposite direction, as shown in FIGS. 10 and 11. This quality is critical for the present invention and its applications.
The fact that not only the group velocity u of the backward wave vanishes at xcfx89=xcexa9, but so does its derivative ∂u/∂k, enhances the property of unidirectionality preventing the frozen wave packet from spreading.
The property of unidirectionality only exists for k∥Z, xcfx89=xcexa9, where Z is the direction of unidirectionality, and xcexa9 is the frozen mode frequency. This means that for directions of wave propagation different from Z and/or for the wave frequencies different from xcexa9, the effect of unidirectionality disappears.
The present invention utilizes the property of electromagnetic unidirectionality in several proposed microwave and optical devices.
In summary, we present the list of the basic terms and definitions we refer to when describing the invention.
A gyrotropic photonic crystal:
is a composite periodic array of two or more constituents each of which does not substantially absorb the energy of ac electromagnetic field in the frequency range of interest. At least one of the constituents must display Faraday rotation. The preferred embodiment of gyrotropic photonic crystals is a periodic magnetic stack, examples of which are shown in FIGS. 5 and 7. In real devices, the total number of the elementary fragments constituting photonic crystal may vary within a wide range starting from just a few.
Bulk spectral asymmetry:
is the property of a homogeneous or periodic composite medium to support an asymmetric dispersion relation xcfx89(k)xe2x89xa0xcfx89(xe2x88x92k) as explained in FIG. 2 or 3. When applied to real systems of finite dimensions, the term spectral asymmetry means the spectral asymmetry of the infinite periodic structure built up of the same primitive fragments as the finite one.
A unidirectional photonic crystal:
is a photonic crystal that transmits electromagnetic waves of a certain frequency xcexa9 propagating in a certain direction Z and, at the same time, it freezes the radiation of the same frequency xcexa9 propagating in the opposite direction, as shown in FIGS. 3 and 11. The frozen wave (mode) is defined as the one having zero or negligible group velocity U, together with its derivative ∂u/∂k. The frequency xcexa9 is referred to as the frozen mode frequency. The direction Z is referred to as the direction of unidirectionality.
A unidirectional slab:
is a fragment of a unidirectional photonic crystal bounded by a pair of plane parallel faces, as shown in FIGS. 10 and 11. This device transmits electromagnetic wave packet with k∥Z and the frequency xcfx89 close to xcexa9 only in one of the two opposite directions along the Z axis, this direction is designated with the arrow 2 in FIGS. 10 and 11. The slab faces are perpendicular to the Z-direction associated with the frozen mode, unless otherwise is specifically qualified.
A tunable photonic crystal:
is a photonic crystal the electromagnetic properties of which, including the electromagnetic band structure, can be controllably altered. The tunability can be achieved by applying or changing external dc or quasi-stationary magnetic or electric field, altering the geometry of the periodic array, or by other external means. In the case of a photonic crystal with spectral asymmetry, the tuning may affect the character and even the very existence of the spectral asymmetry.
The invention is defined as a nonreciprocal unidirectional photonic crystal, which is a periodic array comprising a plurality of at least two constitutive components each of which is practically lossless at electromagnetic frequency range of interest. At least one of the constitutive components is a ferromagnet, a ferrite, or it has a magnetization induced by an applied external magnetic field, so that this component displays substantial Faraday rotation at the frequency range of interest. The composition and the geometry of the periodic array are designed so that the array displays the property of bulk spectral asymmetry and, at least at one particular frequency xcexa9, it also displays the property of electromagnetic unidirectionality.
The invention also comprises an assembly of a unidirectional photonic crystal and some passive or active electromagnetic network elements, for example, a resonator, an antenna or antenna array, a microwave circuitry.
The invention may further comprise a means for providing photonic crystal tunability by controlled altering its electromagnetic characteristics, such as: (i) the frequency xcexa9 of the frozen mode; (ii) the direction Z of unidirectionality; (iii) the degree of spectral asymmetry, which includes the possibility of blurring or eliminating the property of unidirectionality; (iv) other electromagnetic characteristics. Examples of means for providing the photonic crystal tunability include but are not limited to: (i) a controlled source of a dc or a quasi-stationary magnetic field with alterable strength and/or direction, which allows to control the magnetic permeability tensor of the gyrotropic constituent; (ii) a controlled source of a dc or a quasi-stationary electric field with alterable strength and/or direction which allows to control the electric permittivity tensor of at least one of the dielectric constituents; (iii) a motor or an array of motors for altering position and/or orientation of the constitutive components of the array. In a broader conception, means for providing tunability may include any external controlled physical cause altering magnetic permeability or electric permittivity of the photonic crystal constituents and/or altering any of the geometric characteristics of the array.
In one embodiment, shown in FIG. 5, the unidirectional photonic crystal is a periodic stack of identical three-layered elementary fragments, where each three-layered fragment L comprises one ferromagnetic or ferrimagnetic layer and two anisotropic dielectric layers with misaligned anisotropic axes.
In another embodiment, shown in FIG. 7, the unidirectional photonic crystal is a periodic stack of identical four-layered elementary fragments, where each four-layered fragment L comprises two ferromagnetic or ferrimagnetic layers with opposite directions of magnetization and two anisotropic dielectric layers with misaligned anisotropic axes. This embodiment has zero bulk magnetization and therefore does not produce demagnetization field.
In still another embodiment the anisotropic dielectric layers of the either of the above two embodiments are replaced with misaligned stock-pile layers made of an isotropic dielectric material, as shown in FIG. 9.
The invention is still further defined as a unidirectional composite slab with frequency and directional selectivity comprised of an unidirectional photonic crystal bounded by two plane faces, as shown in FIGS. 10 and 11. Each of the two plane faces is perpendicular to the direction Z of unidirectionality, such that a first wave packet 9 of frequency xcexa9 and normal incidence impinging on one plane face enters the slab and freely propagates further through the slab in the same direction as shown in FIG. 10, while a second wave packet 10 of the same frequency xcexa9 and the opposite direction of propagation impinging on the opposite face of the slab 11 gets trapped after entering the slab and its amplitude increases sharply as shown in FIG. 11.
The invention may further comprise the unidirectional slab and a plane mirror parallel to slab faces as shown in FIG. 13. A gap being defined between the mirror and the nearest face of the unidirectional photonic crystal. The mirror is arranged and configured to be sufficiently reflective in a frequency range of interest which includes frequencies in the vicinity of the frozen mode frequency xcexa9.
In one of the embodiments the gap between the mirror and the face has a size of zero and the unidirectional device is used as a wave packet delay line having a delay time xcfx84, as shown in FIG. 14. The delay time xcfx84 is sensitive to the frequency, xcfx89, and to the direction of propagation of the incident wave packet 9. The delay time xcfx84 is maximal when incoming wave packet 9 has normal incidence and a frequency close to the frozen mode frequency xcexa9, in such a case the electromagnetic wave packet after being reflected from the mirror 18, very slowly propagates backward through the unidirectional slab 11 until it escapes the system. The delay line may further comprise means for photonic crystal tunability. In this latter case the delay time xcfx84 can be controllably altered within wide limits.
The invention is even still further defined as a unidirectional single mode resonator with directional and frequency selectivity comprised of a unidirectional photonic slab 11 and a mirror 18, as shown in FIG. 15. The incoming radiation 16 of frequency xcexa9 of the frozen mode and normal incidence impinging on one face of the photonic slab 11 is transmitted through the slab until it reaches the mirror 18. After being reflected from the mirror 18, the radiation is converted into the frozen mode and gets trapped at the rightmost portion of the slab 11 where the electromagnetic radiation accumulates until is further processed. The directional and the frequency selectivity of the device is provided by the fact that the resonator only accumulates the energy of incoming radiation with the frequency xcexa9 of the frozen mode and the normal incidence. The incoming electromagnetic radiation of different frequency or with different direction of propagation, is not converted into the frozen mode after being reflected by the mirror 18 and, therefore, escapes the system.
In such an embodiment the unidirectional single mode resonator in FIG. 15 may further comprise other devices utilizing the accumulated energy. For example, it may further comprise a means for processing of electromagnetic radiation disposed in or near the gap between the mirror 18 and the unidirectional slab 11. Examples of processing means are: a receiving antenna or phase sensitive antenna array 20, a nonlinear element or an array of nonlinear elements, other active and passive elements of optical or microwave circuitry.
The unidirectional resonator may further comprise means for tuning to control: (i) the selected direction of the incoming radiation for which the electromagnetic energy gets trapped in the vicinity of the mirror; (ii) the frequency xcexa9 of the frozen mode; or (iii) the level of directional and frequency sensitivity of the device. Examples of tunability means have been specified earlier.
While the apparatus and method has or will be described for the sake of grammatical fluidity with functional explanations, it is to be expressly understood that the claims, unless expressly formulated under 35 USC 112, are not to be construed as necessarily limited in any way by the construction of xe2x80x9cmeansxe2x80x9d or xe2x80x9cstepsxe2x80x9d limitations, but are to be accorded the full scope of the meaning and equivalents of the definition provided by the claims under the judicial doctrine of equivalents, and in the case where the claims are expressly formulated under 35 USC 112 are to be accorded full statutory equivalents under 35 USC 112.